In "A Modest Proposal," in paragraphs one through five, Swift uses the term, "mother." In paragraph six, he changes this to what word?
You are right in identifying that in paragraph six Swift cleverly uses a different word to describe the "mothers" that have gone before in previous paragraphs. Clearly the diction that Swift employs is key to his overall success in overtly presenting a serious and reasonable "proposal" whilst at the same time highlighting the shocking and dehumanising way in which many of his contemporaries viewed, treated and thought of the Irish. Note the example that you refer to:
The number of souls in Ireland being usually reckoned one million and a half, of these I calculate there may be about two hundred thousand couples whose wives are breeders, from which number I subtract thirty thousand couples, who are able to maintain their own children, although I apprehend there cannot be so many under the present distresses of the kingdom, but this being granted, there will remain an hundred and seventy thousand breeders.
The word "mothers" has been exchanged for "breeders," which clearly suggests a view where Irish women are dehumanised and viewed only for their ability to "breed" in the same way that animals are referred to. Note how Swift uses this term ironically; he is actually reinforcing the point that women are not animals but human beings, but highlighting the way in which they are being treated like animals at the moment.